30th of the MonthDate: 06/18/2001 at 10:10:50 From: selim Subject: Calendar tricks Hi, My question is, what day does the 30th of the month most often fall on (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday)? Date: 06/18/2001 at 12:14:56 From: Doctor Peterson Subject: Re: Calendar tricks Hi, Selim. This will take some work, but you can get ideas for approaching the problem from this similar question, about which day of the week is more common for Jan 1: Years That Start on Sunday http://mathforum.org/dr.math/problems/lane.10.2.00.html Also, check our Calendar FAQ: The Calendar and the Days of the Week http://mathforum.org/dr.math/faq/faq.calendar.html If you need more help, please write back and show me the work you have done. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/18/2001 at 12:48:47 From: Doctor Rob Subject: Re: Calendar tricks Thanks for writing to Ask Dr. Math, Selim. The Gregorian calendar repeats with a period of 400 years. This period of time contains D days, where D = 400*(365 + 1/4 - 1/100 + 1/400), = 146097, 20871 weeks, and 4800 months. 4400 of these months contain a 30th. There are 14 different yearly calendars, 7 for regular years (R) and 7 for leap years (L) (7 because January 1 can fall on any of the 7 days of the week). Here is a table of how many 30ths fall on each day of the week for each of the 14 calendars: Type num Sun Mon Tue Wed Thu Fri Sat ---- --- --- --- --- --- --- --- --- R, Sun 43 2 2 1 1 2 1 2 R, Mon 42 2 2 2 1 1 2 1 R, Tue 44 1 2 2 2 1 1 2 R, Wed 42 2 1 2 2 2 1 1 R, Thu 44 1 2 1 2 2 2 1 R, Fri 42 1 1 2 1 2 2 2 R, Sat 43 2 1 1 2 1 2 2 L, Sun 15 2 3 1 1 1 2 1 L, Mon 14 1 2 3 1 1 1 2 L, Tue 14 2 1 2 3 1 1 1 L, Wed 15 1 2 1 2 3 1 1 L, Thu 13 1 1 2 1 2 3 1 L, Fri 16 1 1 1 2 1 2 3 L, Sat 13 3 1 1 1 2 1 2 --- --------------------------------------- 400 625 632 625 632 627 628 631 = 4400 So it seems that the 30th of the month occurs most frequently on Monday or Wednesday (632/4400 = 14.3636% of the time), and least frequently on Sunday or Tuesday (625/4400 = 14.2045%). - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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